Explain why multiplying by 8/3 gives the same result as first multiplying by 8 and then multiplying by 1/3

Answer:

(- 2, 0 ) , (1, - 3 )

Step-by-step explanation:

the solutions to the system of equations are at the points of intersection with the curve and the straight line.

points of intersection are at (- 2, 0 ) and (1, - 3 ) , then

solutions are (- 2, 0 ) , (1, - 3 )

Answer:

8y

Step-by-step explanation:

Lets put these two parts into addition to make it easier.

(y)56x + 16y^2

(8y)7x + 2y^2

8y is the GCF(grates common factor)

1. The equation of the form y = a • bˣ is y = 81 x (¹/₃)ˣ

2. His stamp should be worth approximately $7,851.47 after 6 years.

3. The equation of the form y = a • bˣ is y = (¹/₁₆) x 2²ˣ ⁺ ⁵

1. One will see that y is decreasing by a factor of 3 as x increases by 1. Therefore, we can write the equation as:

y = 81 x (¹/₃)ˣ

2. The increase in value of the stamp can be calculated using the formula:

V = P(1+r)ᵗ

where V is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.

Substituting the given values:

V = 4900(1+0.075)⁶

V ≈ $7,851.47

Therefore, the stamp should be worth approximately $7,851.47 after 6 years.

3. One will see that y is increasing by a factor of 2 as x increases by 1. Therefore, we can write the equation as:

y = (1/16) x 2²ˣ ⁺ ⁵

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Answer:

60

Step-by-step explanation:

180 - 120 = 60

The condition that will prove the two triangles similar is

side JL = 8 * side ZX

angle L = angle Z

Similar triangles are  triangles which have the  similar shape however not necessarily the equal size. More officially, two triangles are comparable if their corresponding angles are congruent and their corresponding aspects are in proportion.

This means that if we had been to scale one triangle up or down uniformly, the ensuing triangle could be much like the original triangle.

In the figure, the scale is 8

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The requried area of the shaded shape is 5 square millimeters.

From the figure,
The area of the green shaded area is given by:
The area of a single square is given as = 1 * 1 = 1 square millimeters.
Now there is 5 square in the shaded region, So the area is given as:

= 5 * 1 = 5 square millimeters.

Thus, the requried area of the shaded shape is 5 square millimeters.

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As far as a 5/1 ARM is concerned, note that the "1" refers to how often the rate can be adjusted after the initial fixed-rate period ends.

A 5/1 ARM is an adjustable rate mortgage loan (ARM) that has a fixed interest rate for the first five years. Following that, the 5/1 ARM transitions to an adjustable interest rate for the remainder of its term. The terms "variable" and "adjustable" are frequently used synonymously.

If you want a low monthly payment and don't expect to stay in your house for long, a 5/1 adjustable-rate mortgage (ARM) loan may be worth considering. For the first five years, rates on 5/1 ARMs are typically lower than rates on 30-year fixed-rate mortgages.

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Equation which can be used to solve for the value of x is

3x° + 2x° + 80 °= 180° .

Straight angle pair is the sum of two or more angles that are in pair of angles that form a straight line is always equal to 180°.

As shown in the diagram angle on the lines are -

3x ° , 80° , 2x° respectively

Sum of all these angle will be equal to 180°.

3x° + 2x° + 80° = 180

The correct equation to find the value of x is 3x° + 2x° + 80° = 180° .

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The value of x in the trapezoid is 2.

The mid points of a trapezoid is a line that goes across from the middle of one leg to the middle of the other leg.

Using the mid point theorem, let's find the value of x in the trapezoid as follows:

PS = 1 / 2 (QR + TU)

PS = x + 33

QR = -6x + 37

TU = 2x + 41

Therefore,

x + 33 = 1 / 2 (-6x + 37 + 2x + 41)

x + 33 =  1 / 2 (-4x + 78)

x + 33 = -2x + 39

x + 2x = 39 - 33

3x = 6

divide both sides by 3

x = 6 / 3

x = 2

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The chambered nautilus is a fascinating marine animal that belongs to the family of cephalopods.

It is notable for its unique, spiral-shaped shell that is divided into a series of chambers.

The nautilus lives in the outermost chamber of its shell, which it can control by adjusting the amount of gas and fluid inside it. This allows the nautilus to regulate its buoyancy and move up or down in the water column.

The nautilus has been around for millions of years and is sometimes called a "living fossil" because of its ancient lineage.

Unfortunately, due to overfishing and habitat destruction, many species of nautilus are now endangered.

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The given question is incomplete, the complete question is:

A chambered nautilus is a marine animal form which family?

The percentage of the total budgeted category is given by

a) Clothing : 12 %

b) Insurance : 3 %

c) Taxes : 22 %

Given data ,

Let the percentage value be represented as A

Now , the value of A is

Let the total budgeted amount be = $ 6,200

Now , the amount for clothing = $ 744

So , the percentage for clothing = 744 / 6200 = 12 %

And , the amount for insurance = $ 186

Now , the percentage for insurance = 186 / 6200 = 3 %

And , the amount for taxes = $ 1,364

So , the percentage for taxes = 1364 / 6200 = 22 %

Hence , the percentages are solved

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Answer:

800 books

problem solving steps：

adults:60%

young people:5%

children=100%-60%-5%

=35%

35%=280 books

1%=280÷35

=8

100%=800

so,there are 800 books

The solution of the equation is x=1/2 and y=1/3

The given equations are

18x+12y=13...(1)

30x+24y=23...(2)

Let us form the matrix form to solve the equation

[tex]\left[\begin{array}{ccc}18&12\\30&24\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}13\\23\end{array}\right][/tex]

Multiply equation (1) with 2

36x+24y=26..(3)

Subtract equation 3 from equation 2

30x+24y-36x-24y=23-26

-6x=-3

x=1/2

Now plug in the value of x in equation 1

18(1/2)+12y=13

9+12y=13

12y=4

y=4/12

y=1/3

Hence, the solution of the equation is x=1/2 and y=1/3

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Answer:

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Step-by-step explanation:

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Based on the given polynomial function, as x approaches positive or negative infinity, the function f(x) = 2x³ - 3x - 4x⁴ + 1 approaches negative infinity.

The end behavior of a polynomial function is determined as follows:

Examine the leading term of the function f(x) = -4x⁴ + 2x³ - 3x + 1

The leading term of the function is -4x⁴.

For large positive values of x, as x approaches positive infinity, the leading term -4x⁴ becomes increasingly negative since x⁴ grows faster than any positive constant.

Therefore, the end behavior of the function as x approaches positive infinity is that f(x) approaches negative infinity.

Similarly, for large negative values of x, as x approaches negative infinity, the leading term -4x⁴ becomes increasingly negative since x⁴ grows faster than any positive constant.

Therefore, the end behavior of the function as x approaches negative infinity is that f(x) approaches negative infinity.

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The area of the triangle is 6 sq units.

The area of the triangle is calculated by applying the following formula;

A = ¹/₂ x b x h

where;

The base of the triangle = 3 - 0 = 3

The vertical height of the triangle = 5 - 1 = 4

Area = ¹/₂ x 4 x 3

Area = 6 sq units.

Thus, the area of the triangle is a function of base and height.

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Answer:

[tex]C. -5.15\cdot10^{13}[/tex]

Step-by-step explanation:

[tex]Common\ ratio\ (r)=\frac{a_{n+1}}{a_n}=(-3)\\\\Sum\ (S_n)=\frac{a(r^n-1)}{r-1}\ \ (r\neq1)\\\\\implies S_n=\frac{1\ (\ (-3)^{30}-1\ )}{-4}\\\\\implies S_n=\frac{205891132094649-1}{-4}\\\\\approx\frac{206\cdot10^{12}}{-4}\\\\\approx-5.15\cdot10^{13}[/tex]

Answer:

B. 1 tick mark represents 0.2 unit

Step-by-step explanation:

Looking at the axis and going over 2 tick marks is .4

.4 /2 = .2

Each tick mark is .2 units

They need to sell at least 13 cups to gain profits.

Here, we have,

Givens

The initial cost is $1.20.

Each cup of lemonade costs 6 cents to make.

May's children sell 10 cents a cup.

First, we need to represents the cost of their investment.

0.06x = 1.20, because each cup costs 6 cents, and the initial costs of all is $1.20.

That means,

x= 20

They can produced 20 cups.

However, they already sell a cup for 10 cents. So, how many cups they need to sell to gain profits? We need to establish a similar relation,

0.10 x = 1.20

 x = 12

This means if they sell 12 cups, they will just cover the investment, that is, zero profits.

Therefore, they need to sell at least 13 cups to gain profits.

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complete question

Mary's children decide to run a lemonade stand to earn some extra money.The cost to start the business is $1.20 and each cup of lemonade costs 6 cents to make. If lemonade sells for 10 cents a cup,how many cups must Mary's children sell to make a profit?----Apply systems of equations

The number of lego planes that can be build in 40 minutes is A = 2.33

Given data ,

Johnny can build in 3 1/2 lego planes in 60 minutes

On dividing the number of planes he can build in 60 minutes (3 1/2) by 60:

From the proportion , we get

To find out how many planes he can build in 40 minutes, we can multiply the amount he can build in one minute by 40:

3.5 / 60 = A / 40

Multiply by 40 on both sides , we get

A = 2.33

Hence , Johnny can build approximately 2.33 lego planes in 40 minutes

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The question that Diondra would ask that does not allow for variability is A. Which movie did her best friend like the most?

The other three questions ("How many awards did each movie win?", "What is the total dollar amount that each movie made from ticket sales?", and "How many weeks did each movie play in the theater?") all offer metrics by which a movie's popularity could be measured, and those measurements could vary from movie to movie.

However, the question about her best friend's favorite movie depends solely on the opinion of one individual, not a variable measure, and therefore doesn't allow for variability.

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The number of students in each row after any number of years, as long as the increase in rows and columns is uniform every year.

Assuming that the increase in rows and columns is uniform every year, we can derive the formula for the number of students in each row as follows:

Let's start with the initial number of rows and columns, which we'll call R0 and C0, respectively, and the number of students in each row, which we'll call S.

After one year, the number of rows and columns will increase by 5, so we'll have R1 = R0 + 5 and C1 = C0 + 5. The total number of students will be R1 x S. We can also express this in terms of the initial number of rows and columns as:

R1 x S = (R0 + 5) x S

Expanding the brackets, we get:

R1 x S = R0 x S + 5 x S

Subtracting R0 x S from both sides, we get:

(R1 - R0) x S = 5 x S

Dividing both sides by 5 x (R1 - R0), we get:

S = 5 / (R1 - R0)

We can use this formula to calculate the number of students in each row after any number of years, as long as the increase in rows and columns is uniform every year.

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Answer:

No, it is not a right triangle.

[tex] \sqrt{ {13}^{2} + \ {18}^{2} } = \sqrt{169 + 324} = \sqrt{493} [/tex]

√493 is not equal to 24.

Answer:

it doesn't

Step-by-step explanation:

it doesn't follow pythagoras theorem

a² = b² + c²

Answer:

Step-by-step explanation:

y=mx+b

m= slope and b= y intercept

you'll start with a point on the y axis on -1

and the slope will go up so towards the right corner up but 2/1 points

The probability that Anita gets a purple tulip and Lois gets a pink rose is 1/9.

Total number of flowers in the bouquet = 7 purple tulips + 9 yellow daisies + 12 pink roses = 28 flowers.

P(Anita gets a purple tulip) = 7 purple tulips / 28 total flowers = 7/28 = 1/4.

P(Lois gets a pink rose) = 12 pink roses / 27 remaining flowers = 12/27 = 4/9.

P(Anita gets a purple tulip and Lois gets a pink rose) = P(Anita gets a purple tulip) * P(Lois gets a pink rose)

= (1/4) * (4/9) = 1/9.

Therefore, the probability that Anita gets a purple tulip and Lois gets a pink rose is 1/9.

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The value of sin(θ) is 0.31 and it lies in the third and fourth quadrants. if the value of the cosine of θ is −0.95.

cos(θ) = -0.95

To calculate the value of sin(θ), we can use the Pythagorean theorem:

[tex]sin^{2}[/tex] (θ) +[tex]cos^{2}[/tex] (θ) = 1

We can rearrange the Pythagorean identity to solve for sin(θ):

[tex]sin^{2}[/tex] (θ)= 1 - [tex]cos^{2}[/tex]

sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)---------  (equation 1)

Substitute the value of the cosine of θ = −0.95 in Equation 1

sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)

sin(θ) = ±[tex]\sqrt{(1 - 0.9025)}[/tex]

sin(θ) = ±[tex]\sqrt{0.0975}[/tex]

The positive value determines that the value is in the first and second quadrants, Negative shows the third and fourth quadrants.

sin(θ) = [tex]\sqrt{ 0.0975}[/tex]

sin(θ) = 0.312

Therefore, we can conclude that the value of sin(θ) is 0.312.

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Answer:

y- intercept = - 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = 2 , then

y = 2x + c ← is the partial equation

to find c substitute (5, 4 ) into the partial equation

4 = 2(5) + c = 10 + c ( subtract 10 from both sides )

- 6 = c

that is the y- intercept c = - 6